Several designs were considered during the development of a working embeddable dual parameter sensor. These designs used combinations of ultrasonic embedding, embedded reinforcements, different adhesive types, and multiple fiber arrangements. First, the design of an external dual parameter sensor will be examined. The three most viable dual param-eter sensor designs will then be examined. The three embedded dual paramparam-eter designs are all based on the silver nanoparticle embedding method. For readability, ’embedded dual parameter sensor’ will be shortened to EDPS.
Single Needle External Dual Parameter Sensor
The first design for an EDPS using silver nanoparticle adhesive was based on the work of T.Y.R. Liang [22]. In [22], a dual parameter FBG sensor was developed using epoxy and a hypodermic needle. This dual parameter sensor was not embedded, it was intended to be used externally. Figure3.5 shows a cross section of the sensor developed in [22].
Figure 3.5: External dual parameter sensor developed by [22].
The idea behind the sensor in Figure 3.5 is to create two distinct regions on the FBG.
Half of the FBG is encapsulated by a sheath made from a hypodermic needle. This needle is adhered to the fiber using epoxy as an adhesive. The two ends of the fiber are attached to anchors using epoxy. The anchors are used to load the fiber and to induce a strain on the fiber.
The two halves of the FBG react differently when a load is applied to the anchors.
The FBG section with the needle is stiffer relative to the FBG section without the needle.
This effectively creates a scenario which is analogous to having two springs with different stiffnesses connected in series. When both sections are put under the same load, the strain on the uncovered FBG section will be larger. A qualitative representation of the axial strain along the length of the fiber is also show in Figure3.5.
Creating these two sections along the length of the FBG with different stiffnesses allows the FBG to have two sections with different effective strain sensitivities. In other words, as load is applied to the anchors in Figure 3.5, the optical interrogator should record two distinct peaks that represent two distinct Bragg wavelengths. An example of a spectrum with peak splitting is shown in Figure 3.6.
Figure 3.6: Example of peak splitting in a dual parameter FBG.
Equation 3.3 describes how the Bragg wavelength of a single FBG will change based on strain and temperature. If multiple FBGs are subject to the same strain/temperature mutiple bragg wavelengths can be recorded. Equation3.19show a matrix Equation relating the two Bragg wavelengths.
Since both FBGs are subject to the same temperature and strain changes, a sensitivity matrix K can be isolated.
As long as the columns of the sensitivity matrix K are linearly independent (i.e.
rank(K)=2), the sensitivity matrix can be inverted and the strain/temperature state of the sensor can be determined from the two recorded Bragg wavelengths.
In other words, to produce a dual paramter sensor, two Bragg wavelength peaks with different sensitivities are recorded simultaneously.
Single Needle Embedded Dual Parameter Sensor
The first design of an EDPS was based on the design from [22] and on the embedding process for single parameter sensors developed in this thesis. As described in Sections3.3.2 and 3.3.1, the embedding procedure consists of first drilling a hole in the host material, then using silver nanoparticle paste as an adhesive to bond the fiber to the host material.
This embedding procedure can be used to embed a dual parameter sensor.
The design of the single needle EDPS is shown in Figure3.7. The single needle EDPS is simply an embedded single parameter sensor with an additional needle around half the FBG. The needle was expected to produce two sections with different strain sensitivities along the length of the FBG, similarly to the single needle external dual parameter sensor.
To have a better understanding of the strain along the length of the FBG, Finite Element Analysis (FEA) was done to give a good estimation fiber axial strain. COMSOL
Figure 3.7: Single needle EDPS.
Multiphysics 4.4 was used as the main FEA software.
The material properties used in the FEA are outlined in Table 3.4. The dimensions of the components in the FEA are outlined in Table3.5.
Table 3.4: Material properties used in FEA.
Material Elastic Modulus(GPa) Poisson’s Ratio
Sintered Silver 15.0 0.37
Silica Glass 73.1 0.17
316 Stainless Steel 205 0.28
AZ31B Magnesium Alloy 45.0 0.29
The entire system was modelled as an axisymmetric model with the symmetric axis at the center of the fiber. All material was assumed to behave in an isotropic, linear elastic manner following Hooke’s law and assuming infinitesimal strain.
Mesh independence analysis was done on all FEA results. The maximum element size used which allowed solution convergence was 30 µm. The MUMPS solver along with the
Table 3.5: Dimension of Components for FEA.
approximate minimum fill preordering algorithm was used. The host material (AZ31B) was put under 20, 40, and 60 MPa axial stress while the fiber and the silver were left unloaded, this loading condition is shown in Figure3.7.
The strain transfer ratio from the FEA of the single needle EDPS is show in Figure 3.8. Strain transfer ratio is the ratio of the strain experienced by the fiber relative to the strain experienced by the host material. In Figure 3.8 the strain transfer ratio is plotted with respect to the length of the embedded portion of the fiber.
In Figure 3.8, the strain transfer ratio from 0 to 5 mm is very similar to the strain transfer ratio described in Figure 3.4. The first 2.5mm of embedded fiber are required to allow the silver to properly transfer strain to the fiber. The section from 2mm to 5mm has a strain transfer ratio of 1. This shows that the strain on the fiber between 2mm and 5mm perfectly matches the strain in the host material.
The section of fiber from 7.5mm to 12.5mm is surrounded by the stainless steel needle.
As previously described, the purpose of the needle was to strengthen the section and to reduce the strain transfer ratio. The needle does not produce the same effect for an embedded sensor as for an external sensor. Near the ends of the needle (at 7.5mm and
Figure 3.8: Strain transfer of a single needle EDPS from FEA.
12.5mm) there are large fluctuations in strain transfer ratio. Along the length of the needle (between 7.5mm and 12.5mm), the strain transfer ratio is not constant. This fluctuating, non-constant behaviour of the strain transfer ratio means that the fiber is not experiencing constant strain in this section.
The main cause of the strain-transfer ratio fluctuations along the needle section is the coupling of the strain from the host material to the needle. Although the needle does reinforce the section and it does reduce the strain transfer ratio near the ends of the needle, the strain transfer ratio still approaches a value of 1 near the center of the needle.
If the needle were long enough, the strain transfer ratio at the center would reach 1. The behaviour can be described analytically using a similar model to the one outlined in Section 3.1.1.
All previous discussion on FEA results has only described the strain transfer along a plain fiber without Bragg grating. We will now consider that the embedded fiber has an
8mm Bragg grating starting at 3mm and ending at 11mm in Figure 3.8.
The first section of the FBG from 3mm to 5mm would experience a strain transfer ratio of 1. The second section of the FBG from 5mm to 11mm would experience a varying strain transfer ratio. This configuration should therefore produce a single strong peak in reflectivity and significant noisy side lobes around the peak.
To quantitatively examine the spectrum produced by this strain distribution along the fiber, the model from Section3.1.3and the Matlab implementation from AppendixAwere used to produce an FBG spectrum.
The spectra produced using the Matlab model had a center wavelength of 1530 nm, a fringe visibility of 1, and a DC index change 10−4. Each spectrum plot shows the predicted reflectivity spectrum of the FBG at 0.1, 0.3, and 0.5 percent strain at ambient temperature.
Figure3.9 shows the reflectivity spectrum for the single needle EDPS. Figures 3.12, 3.15, and 3.18 were produced using the same parameters as the spectrum in Figure3.9.
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Figure 3.9: Reflectivity spectrum of single needle EDPS.
As expected, there is only one discernible peak and significant side lobe noise for all simulated strains in Figure 3.9. Two clearly detectable peaks with differing sensitivities
are necessary to be able to determine the strain-temperature state of the system using Equation3.20. The single needle EDPS was not constructed due to this result.
Double Needle Embedded Dual Parameter Sensor
The main issue with the single needle EDPS was the strain transfer of the host material to the fiber through the needle. The double needle EDPS design attempted to eliminate the shear strain transfer through the needle.
To eliminate the undesirable strain transfer effects, an outer needle was added to the design of the EDPS as shown in Figure 3.10. Essentially, the double needle EDPS is a single needle external dual parameter sensor encased in a protective outer needle. The main purpose of the outer needle is to prevent the silver adhesive from bonding to the FBG and the inner needle by creating an interlayer of air between the inner and outer needle.
Figure 3.10: Double needle EDPS.
The air interlayer eliminates any strain transfer from the host material to the FBG through shear. All strain is axially transfered to the FBG from the ends of the fiber that
are bonded to the silver adhesive beyond of the outer needle.
To determine strain distribution along the length of the double needle EDPS, FEA was done. All material parameters for the FEA were taken from Table 3.4. Dimensions were taken from Table 3.5 with the addition of a 10 mm long, 22 gauge needle (717.6 µm OD, 413 µm ID). All other FEA parameters and procedures were identical to those in Section 3.3.3. The result of the FEA is shown in Figure 3.11.
Figure 3.11: Strain transfer of a Double needle EDPS from FEA.
The double needle design produces two regions with different strain transfer ratios.
The uncovered section of FBG experiences a strain transfer ratio of 1.6. This large strain transfer ratio means that the uncovered section of the FBG should be more sensitive to strain than than the covered section which experiences a strain transfer ratio of 0.1. This result shows that the air interlayer successfully eliminates the undesirable strain effects that were present in the single needle EDPS.
The transition section between the uncovered section and the covered section of the
FBG is limited to 0.6mm of the fiber length. If a sufficient fraction of the FBG is experi-encing constant strain in either the covered or uncovered section, the resulting spectrum should have limited side lobe noise.
We will now consider that an FBG is placed from 3mm to 11mm along the length of the fiber from Figure3.11. The optomechanical model from Appendix Awas used to produce a reflectivity spectrum for the double needle EDPS. The reflectivity spectrum is shown in Figure3.12.
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Figure 3.12: Reflectivity spectrum of double needle EDPS.
The spectra in Figure 3.12 show two clear peaks forming with increasing strain. The presence of two clearly identifiable peaks shows that this FBG configuration may be used as dual parameter sensor at higher strain. At 0.1% strain, however, two peaks cannot be clearly identified and determination of the strain-temperature state may be difficult.
A prototype of the double needle EDPS was constructed due to the promising results from the FEA and optomechanical modeling. All materials and dimensions were identical to those used in section 3.3.3 and in Tables 3.4 and 3.5. The embedding procedure was
identical to the procedure described in Section 3.3.2 with the addition of both inner and outer needles. The needles were first positioned, silver paste was then applied to the appropriate areas of the double needle EDPS.
Although analytical and numerical modeling of the double needle EDPS design showed promising results, the double needle design was found to have two major flaws. Due to the small size of the inner needle and the high viscosity of the silver paste, reliably depositing silver paste between the inner needle and the fiber was extremely difficult.
Additionally, manipulation of multiple needles and maintaining then air interlayer before sintering was challenging. Despite the impractical assembly procedure, several prototypes were successfully assembled and sintering was attempted.
The sintering of the double needle EDPS’s demonstrated another major flaw in their design. After the sintering of the prototype was complete, the EDPS was allowed to cool to ambient temperature. During the cooldown phase, all 6 double needle EDPS prototypes failed suddenly and all reflectivity peaks disappeared. The cause of the sudden loss of signal during cooldown was attributed to the difference in the coefficient of thermal expansion between the glass fiber and metallic host material.
During the sintering stage of the embedding process, the entire host part, fiber, needles, and silver is heated to 260◦C before bonding occurs. AZ31B has a coefficient of thermal expansion 26 µm/m◦C while fused silica glass fibers has a coefficient of thermal expansion of 0.54 µm/m◦C [54]. Once the sintering is complete, the fiber should be under relatively little strain, however, as the metallic host part cools down it will experience significantly more compressive strain than the glass fiber due to their differing coefficients of thermal expansion. Sections of the glass fiber are not supported by any material in the double EDPS and can therefore be prone to buckling and fracture if excessive mechanical compressive strains are applied to the fiber by the host material. Buckling of the unsupported fiber
due to differing coefficients of thermal expansion was presumed to be main failure mode.
Single Needle Floating End Embedded Dual Parameter Sensor
The lessons learned from previous EDPS designs were taken into account and a list of design requirements was formulated to guide a new design for an EDPS.
The critical design requirements are as follows:
• There must be two FBG sections with different but constant strain transfer ratios to produce two clear peaks in the reflectivity spectrum
• The transition region between the FBG sections with different strain transfer ratios should be small to avoid noise in the produced reflectivity spectrum
• To avoid fiber buckling, there should be no unsupported sections of fiber that can be exposed to compressive strain
• To simplify assembly, the number of needles should be minimized and no silver should be placed between a needle and the fiber
With these new criteria, the single needle, floating end EDPS was designed. This design will be referred as the ”floating EDPS” for simplicity. Figure 3.13 shows a diagram of the floating EDPS.
The design of the floating EDPS only contains a single needle and no silver is placed between a needle and the fiber. This simplified design allows for easier assembly during the embedding process. A section of fiber is protected by a needle to allow a air interlayer between the fiber and the host material. The fiber terminates inside the needle to create
Figure 3.13: Single needle floating end EDPS.
the so called ”floating” end of the fiber. The floating end should have a strain transfer ratio of zero because it is not connected to the host material.
Figure 3.14: Strain transfer of a single needle floating end EDPS from FEA.
FEA was performed to determine the strain transfer ratio along the length of the fiber for the floating EDPS. All material parameters for the FEA were taken from Table 3.4.
Dimensions were taken from Table3.5with the fiber prematurely terminated 0.5 mm before
the end of the needle. All other FEA parameters and procedures were identical to those done in Section3.3.3. The result of the FEA is shown in Figure 3.14.
As expected, the FEA indicates that the floating end of the fiber exhibits a strain transfer ratio of 0. The bonded section of the fiber has a strain transfer ratio of 1 between 2mm and 5mm. There is a transition section of non-constant strain transfer between 6mm and 7.5mm. To effectively capture the strain at both the floating section and the bonded section, a FBG was assumed to be placed from 3mm to 11mm. The reflectivity spectrum resulting from this FBG was determined using the optomechanical model described in Appendix A along with the same optical parameters as described in Section 3.3.3. The spectrum for the floating end EPDS is shown in Figure3.15.
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Figure 3.15: Reflectivity spectrum of single needle floating end EDPS from model.
The appearance of two clear Bragg wavelength peaks can be seen in Figure 3.15 at 0.3% and 0.5% strain. These peaks along with Equation3.20can be used to determine the strain-temperature state of the sensor. At 0.1% strain, two peaks are not clearly visible and there is some side lobe noise likely cause by the transition section of the floating end
EDPS. This noise and the lack of two peaks at low strain may cause problems when trying to determine the strain-temperature state of the sensor.
A prototype of the floating needle EDPS was constructed using the same materials and dimensions used in the FEA and the optomechanical model of the floating needle EDPS.
The embedding procedure was identical to the one described in3.3.2 with the addition of the single needle. The floating needle EDPS assembly was simple and more practical than the double needle EDPS assembly. There was no loss of signal during the sintering process or during the cooldown of the sensor. Due to the difference in the coefficients of thermal expansion between glass and AZ31B, a comnpressive strain of -0.6% was expected. This compressive strain created during cooldown should result in the creation of two clear Bragg wavelength peaks at room temperature. The actual reflectivity spectrum of the floating end EDPS is shown in Figure3.16.
Wavelength
Figure 3.16: Reflectivity spectrum of single needle floating end EDPS prototype.
Only a single peak is identifiable in Figure 3.16. A noticeable plateau beside the peak can also be identified. The single peak is produced by the floating end of the FBG and
the plateau is likely cause by the bonded section of the FBG. A plateau of this kind may be caused by a very large transition period which has non-constant strain transfer. This non-constant strain can spread out the second Bragg wavelength peak and turn it into a plateau rather than a clear peak. In the FEA and the optomechanical model, perfect bonding is assumed between the fiber and silver. In practice, the transition region may be larger due to imperfect bonding. Imperfect bonding and an increased transition region of non-constant strain transfer was presumed to be the cause of the plateau. Several floating EDPS prototypes were constructed with similar results.
To eliminate the plateauing of the second Bragg wavelength peak, the floating EDPS
To eliminate the plateauing of the second Bragg wavelength peak, the floating EDPS